We study the evolution of cooperation by quantifying the chance that a single mutant type, introduced at a random node, will eventually spread and overtake the entire population.
We assume that the population structure for strategy dispersal is strongly connected, meaning that for any pairs of \(i,j\in \mathcal {N}\)  there is a directed path from \(i\)  to \(j\)  in strategy dispersal networks. Letting \(\rho _C\)  (respectively \(\rho _D\) ) denote the probability that a single mutant cooperator (respectively defector) eventually overtakes the population, we say that selection favors cooperation over defection provided \(\rho _C>\rho _D\)  [1]}.
